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80
CHAPTER 2
Nonlinear Functions
vertically 3 units, as compared to the graph of y 5 22x. Since y 5 22x would have yintercept 1 0, 21 2 , this function has y-intercept 1 0, 2 2 , which is up 3 units. For negative
values of x, the graph approaches the line

Parametric Equations and Polar Coordinates
In this section , we extend the concepts of calculus to
curves described by parametric equations and polar
coordinates. For instance, in order to study the motion of
an object such as an airplane in two dimension

774
CHAPTER 9
.
Parametric Equations and Polar Coordinates
9-60
y2
x2
+
= 1,
35. In example 6.9, if the shape of the reector is
124 24
how far from the kidney stone should the transducer be
placed?
the spectator. If the objects distance from the spectator

786
CHAPTER 10
.
Vectors and the Geometry of Space
10-2
As you will see in the exercises in section 10.3, the banking of a road changes the role of gravity. In effect, part of the weight of the car is diverted into a force that helps the car make its turn

716
.
CHAPTER 9
9.1
Parametric Equations and Polar Coordinates
9-2
PLANE CURVES AND PARAMETRIC EQUATIONS
We often nd it convenient to describe the location of a point (x, y) in the plane in terms of
a parameter. For instance, in tracking the movement of a

9-41
SECTION 9.5
9.5
.
Calculus and Polar Coordinates
755
CALCULUS AND POLAR COORDINATES
Having introduced polar coordinates and looked at a variety of polar graphs, our next step
is to extend the techniques of calculus to the case of polar coordinates. I

Vectors and Geometry in Space
To locate a point in a plane, two numbers are
necessary. We know that any point in the plane can be
represented as an ordered pair ( a, b) of real numbers,
where a is the x-coordinate and b is the y-coordinate.
For this reaso

IIUM, Faculty of Engineering,
Department Engineering in Science
Engineering Calculus II, MTH 1212,
Chapter I.4: Polar Coordinates
1.4 POLAR COORDINATE
A coordinate system represents a point in the plane by an ordered pair of numbers
called coordinates. Us

IIUM, Faculty of Engineering,
Department Engineering in Science
Engineering Calculus II, MTH 1212,
Chapter II.3: L&P in space. Quadric Surface
2.3 LINE and PLANES in SPACE. QUADRIC SURFACE
The Lines and Planes in Space:
We now take the question of finding

Jim Lambers
MAT 169
Fall Semester 2009-10
Lecture 29 Notes
These notes correspond to Section 9.1 in the text.
Parametric Curves
There are many useful curves that cannot be described by an equation of the form = (), because
is a function and therefore req

Chapter 1: Finance Mathematics
Lecture 2: Continuous Money Flows
by Associate Professor Pham Huu Anh Ngoc
Motivation
Question: Given a changing rate of annual income and a certain rate of
interest, how can we nd the present value of income?
Earlier, we co

Finance Mathematics
Lecture 3: Annuities
by Associate professor Pham Huu Anh Ngoc
Motivation
Example
Suppose $1500 is deposited at the end of each year for the next 6 years
in an account paying 8% per year, compounded annually. How much will
be in the acc

Calculus 2-BA
Lecture 3&4: Maxima and Minima, Total Dierentials
April, 2015
Maximum and minimum: Motivation Examples
Example 1: The prot from the sale of x units of radiators for
automobiles and y units of radiators for generator is given by
P(x, y ) = x

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